Abstract
We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We ask whether the diameter of such a metric is finite or infinite. The first answer we interpret as an abundance of closed geodesics, while the second one as their scarcity. We discuss examples for both cases.
Original language | English |
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Pages (from-to) | 523-530 |
Journal | Geometriae Dedicata |
Volume | 213 |
Early online date | 28 Jan 2021 |
DOIs | |
Publication status | Published - 31 Aug 2021 |
Bibliographical note
Open Access via the Springer Compact AgreementAcknowledgements This work was partly funded by the Leverhulme Trust Research Project Grant RPG-2017-159. MM is supported by the grant Sonatina 2018/28/C/ST1/00542 funded by Narodowe Centrum Nauki. MM and JK were partially supported by SFB 1085 “Higher Invariants” funded by Deutsche Forschungsgemeinschaft.
Keywords
- math.DG
- math.GR
- math.GT